Thus we see that while the expected step size is of order \(\Delta \bar{\chi }_{x}\sim 1/\alpha _{x}\) , the fluctuations go as \(\Delta w_{x}\sim 1/\alpha _{x}^{1/2}\) . Thus, for short steps, i.e. \(\alpha _{x}\rightarrow \infty \) , the fluctuations overwhelm the drift, resulting in a trajectory that is continuous but not, in general, differentiable. Such a model describes a Brownian motion in the field variables \(\chi _{x}\) .As discussed in [1]}[2]}, with appropriate choices of the multipliers \(\alpha \)  and \(\alpha ^{\prime }\)  the fields or the particles, as the case might be, can be made to follow paths typical of a Brownian motion or alternatively paths that are smooth and resemble a Bohmian motion. It is remarkable that these different paths at the sub-quantum level all lead to the same Schrödinger equation.
